Added prime-omega

collects/math/private/number-theory/number-theory.rkt

@@ -23,6 +23,7 @@
          divisors
          prime-divisors
          prime-exponents
+         prime-omega
          
          ; roots
          integer-root
@@ -489,6 +490,12 @@
   (map (inst cadr N N (Listof N)) 
        (prime-divisors/exponents n)))
 
+(: prime-omega : N -> N)
+; http://reference.wolfram.com/mathematica/ref/PrimeOmega.html
+(define (prime-omega n)
+  (for/fold: ([sum : Natural 0]) ([e (in-list (prime-exponents n))])
+    (+ sum e)))
+
 
 (: integer-root/remainder : N N -> (Values N N))
 (define (integer-root/remainder a n)

collects/math/scribblings/math-number-theory.scrbl

@@ -539,6 +539,15 @@ all divisors of @racket[n].
                     (apply + (map sqr (divisors 12)))]
 }
 
+@margin-note{OEIS: @hyperlink["http://oeis.org/A001222"]{Big Omega}}
+@defproc[(prime-omega [n Natural]) natural?]{
+Counting multiplicities the number of prime factors of @racket[n] is returned.
+
+Note: The function @racket[prime-omega] is multiplicative.
+
+@interaction[#:eval untyped-eval         
+                    (prime-omega (* 2 2 2 3 3 4 5))]
+}
 
 @; ----------------------------------------
 @section[#:tag "number-sequences"]{Number Sequences}